In the hardware user guide, the pinout is very strange. It says:
1 NC
2 NC
3 RXD
4 GND
5 GND
6 TXD
7 NC
8 NC
But for terminal connection you need more than just rxd und txd. even if they mean 3-->RXD+ 4-->RXD-,... this woult be strange, wouldn´t it?

The pinout in the hardware guide is correct. For a serial cable, you need only 3 signals - send, receive, signal ground, and ready, which is itself shorted to ground in the absence of flow control (ie, "always ready"). There is no +/- because the signal is not balanced.

But they [RJ45 pins] ar number this way, if i get it wright now:
8 6 4 2
7 5 3 1

Yes, that is right.

Are there some ideas, what i can try to get the Switches back to live? I cant imagine, that all 3 Switches wont work at all. Even no console output. There mut be sth wrong. Please help!

Agreed...any kind of schematic, hint as to what might be wrong, or direction to begin troubleshooting would be very welcome. I tried opening the switch and there were a great many jumpers all over the place. My guess is that a capacitor somewhere needs to be replaced, or maybe solder reflowed or perhaps a flash chip replaced. With other switches, the main unfixable problem is switch fabric deterioration, which usually causes several ports to go bad well before the switch blows up.

It's frustrating that so little information is available about Alcatel's products. The switches themselves seem decent, but I can understand why everyone seems to rate Alcatel as the vendor of last resort.